A few versions ago, MC library file format was changed, so older library files (a library consists of MANY MC files) are not directly usable by newer MC. But the media files themselves are usable.
I'm not sure what you want to do, but if you want to run MC14 and MC22 together, here are some tips. I currently use MC15 (for its tagging capabilities) and MC21/22 (for everything else) on the same PC with the same library...carefully. I'm pretty sure MC14 used the same library format as MC15.
Of course, each MC (MC15, MC21, MC22 all installed on same PC right now) has its own set of program files. My library files are always in a custom location (not where MC default puts them), but each MC version uses a different custom location (all next to each other for easy management by me). The above are one-time-per-MC version steps.
All my media files (audio files in my case) are in just one location...also a custom location set by me. So, there are (currently) 3 versions of MC installed, but just ONE media storage location shared by all the MCs.
Each MC is set to store tags in the media files. This is key. And each MC is set to Auto-Import from the storage location they all share (including subfolders). After that, it just works.
If I change a track's file tag in MC15's library, the tag gets updated in the audio file (.flac, typically, but the same happens with .mp3 and other formats). MC22 notices the file change and updates its library by reading the updated tag from the file. Automatically.
If I add a file to the library in MC22, MC15 (thanks to auto-import) quickly discovers the new file and adds it too.
I even run MC15 and MC21/22 simultaneously, doing all my file work (ripping, converting, analyzing audio, etc) in the newest MC, but do tagging of the same tracks in MC15.
Just my goofy system, devised to meet my needs, but indication of what can be done.
OR, if the need is just a one-way migration from MC14 to MC22, I think making an MC14 library backup then loading it in MC22 works smoothly. The trick then is to be sure the media file storage location is as-desired, which can require a little dance with MC's Library Manager defaults. (I never use MC's default library name or paths, I always set up a new library, easy to control its name and storage path.)
PS: For photos management I run MC21/22 simultaneously with Google Picasa (Windows version, not the online thing), pointing to the same photos storage, because they each provide useful capabilities the other lacks. Mainly, MC is used for photo organization, captioning, tagging, Picasa for simple image correction such as straightening and cropping (and sometimes date/time correction because it can adjust a bunch of photos via offset not single-value). It's cool to have both apps open at the same time, same set of photos on-screen. For instance, I notice a crooked photo, straighten it in Picasa, and within seconds the MC screen updates with the changed photo. In MC I add captions to 100 photos in one step; Picasa would require 100 steps. Then immediately Picasa shows the new captions. Pretty cool.